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A continuous spectral algorithm and computer routines in the R programming environment that enable the simulation of second-order stationary and intrinsic (i.e., with second-order stationary increments or generalized increments) vector Gaussian random fields in Euclidean spaces are presented. The simulation is obtained by computing a weighted sum of cosine and sine waves, with weights that depend on the matrix-valued spectral density associated with the spatial correlation structure of the random field to simulate. The computational cost is proportional to the number of locations targeted for simulation, below that of sequential, matrix decomposition and discrete spectral algorithms. Also, the implementation is versatile, as there is no restriction on the number of vector components, workspace dimension, number and geometrical configuration of the target locations. The computer routines are illustrated with synthetic examples and statistical testing is proposed to check the normality of the distribution of the simulated random field or of its generalized increments. A by-product of this work is a spectral representation of spherical, cubic, penta, Askey, J-Bessel, Cauchy, Laguerre, hypergeometric, iterated exponential, gamma, and stable covariance models in the d-dimensional Euclidean space. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of simulating multivariate random fields with stationary Gaussian increments in a d-dimensional Euclidean space. To this end, one considers a spectral turning-bands algorithm, in which the simulated field is a mixture of basic random fields made of weighted cosine waves associated with random frequencies and random phases. The weights depend on the spectral density of the direct and cross variogram matrices of the desired random field for the specified frequencies. The algorithm is applied to synthetic examples corresponding to different spatial correlation models. The properties of these models and of the algorithm are discussed, highlighting its computational efficiency, accuracy and versatility. [ABSTRACT FROM AUTHOR]

This work pertains to the simulation of an intrinsic random field of order $$k$$ with a given generalized covariance function and multivariate Gaussian generalized increments. An iterative algorithm based on the Gibbs sampler is proposed to simulate such a random field at a finite set of locations, resulting in a sequence of random vectors that converges in distribution to a random vector with the desired distribution. The algorithm is tested on synthetic case studies to experimentally assess its rate of convergence, showing that few iterations are sufficient for convergence to take place. The sequence of random vectors also proves to be strongly mixing, allowing the generation of as many independent realizations as desired with a single run of the algorithm. Another interesting property of this algorithm is its versatility, insofar as it can be adapted to construct realizations conditioned to pre-existing data and can be used for any number and configuration of the target locations and any generalized covariance model. [ABSTRACT FROM AUTHOR]

During October and November 1998 (rainy season), and December, February and March 1999 (dry season), larvae distribution of Petrolisthes armatus and associated decapods were sampled in three different sites at the Punta Morales peninsula, Gulf of Nicoya, Costa Rica. A total of 6014 decapod larvae were collected, and 73 belonged to the genus Petrolisthes spp. No significant total larval density differences were found between seasons (p>0.05); but there was a greater density of P. armatus and other decapod larvae (p>0.05) during the dry season. In addition, no significant variations on temperature and oxygen concentration were observed. P. armatus larval abundance was higher during low tide, in contrast with other decapod larvae. Significant differences among sites were found for other decapod larvae, but not for P. armatus. The only parameter that varied significantly between seasons was salinity and results demonstrate that this factor regulates temporal concentration of larvae. Moreover, flow-tide oscillations were the most important spatial factor in larval dynamics. We propose this mechanism: P. armatus liberates larvae during high tide; these larvae leave the coastal area during low tide and return to the rocky intertidal ecosystem during high tide, when they are ready to settle as megalopa (pre-juvenile stage). Parallel laboratory observations showed higher survival rates at lower salinities (15 ups against 35 ups) and that the duration of the period from zoea I to megalopa was, in average, 19 days. [ABSTRACT FROM AUTHOR]

During October and November 1998 (rainy season), and December, February and March 1999 (dry season), larvae distribution of Petrolisthes armatus and associated decapods were sampled in three different sites at the Punta Morales peninsula, Gulf of Nicoya, Costa Rica. A total of 6014 decapod larvae were collected, and 73 belonged to the genus Petrolisthes spp. No significant total larval density differences were found between seasons (p > 0.05); but there was a greater density of P. armatus and other decapod larvae (p > 0.05) during the dry season. In addition, no significant variations on temperature and oxygen concentration were observed. P. armatus larval abundance was higher during low tide, in contrast with other decapod larvae. Significant differences among sites were found for other decapod larvae, but not for P. armatus. The only parameter that varied significantly between seasons was salinity and results demonstrate that this factor regulates temporal concentration of larvae. Moreover, flow-tide oscillations were the most important spatial factor in larval dynamics. We propose this mechanism: P. armatus liberates larvae during high tide; these larvae leave the coastal area during low tide and return to the rocky intertidal ecosystem during high tide, when they are ready to settle as megalopa (pre-juvenile stage). Parallel laboratory observations showed higher survival rates at lower salinities (15 ups against 35 ups) and that the duration of the period from zoea I to megalopa was, in average, 19 days.